hmm...here are a few F shapes to try, hopefully you can read tab:

e-8----5--------------
b-10---6--7-----------
g-10---5--8-----------
d-10---7--7-----------
a-8----8--------------
E---------7-----------

That last chord is a tritone substitute, a B7 chord. B is the flat 5 to the F, so they sound pretty bad played together. i dont reccommend using the B7 chord in either of those songs, but im just making you aware that there are all kinds of ideas and substitutes to use. Such as:

e--------5---0---------------
b--8-1-1-5--1-----------------
g--9-2-0-5--2-----------------
d--7-2-2-7--3-----------------
a--8-----8--------------------
E----1-1----------------------

These chords are in this order: Fmaj9, Fmaj7, Fmaj6, Fmaj7, and Fmaj7. All the different Fmaj7 are the same chord, but fingered differently. They all have the 1357 chord structure to make it a Fmaj7 chord. You should try all the different Fmaj7 fingerings to see which one you prefer to finger.

Hope this helps you. :)

Edit: Oh yeah, if you want to use the open F chord, you should work on your technique. Make sure your fingers arent diagonal across the fret board. your first finger on the F chord should stay straight on the first fret. Your 2nd and 3rd finger must be in this position, only being the fret area they are assigned, but make sure they are arched so they dont make contact with the other strings. Also, center your thumb on the back of the neck when starting. This discipline was hard for me starting out, but im glad i did it. I know mostly play with my thumb resting where the fretboard and neck meet, where the little dots are if you have them, except on power chords, where you must keep perfect position. excuse me for using the basic term power chord. it really is a two note 1 5 diad chord, i think, correct me if Im wrong. Oh, some of those chords up there i showed don't have to have your thumb on the back of the neck, just so you know if you struggle doing that. And another thing, make sure your fingers on your left hand are right up to the fret to prevent buzzing. Trust me, if you start out playing with good technique, youll soar farther than you ever thought you would. Hope this helps as well. :)